This talk will start by the presentation of my PhD work, concerned with the study of a Discontinuous Galerkin Time-Domain method (DGTD), for the numerical resolution of the unsteady Maxwell equations on hybrid tetrahedral/hexahedral in 3D (triangular/quadrangular in 2D) and non-conforming meshes, denoted by DGTD-PpQk method. Like in several studies on various hybrid time domain methods, the general objective is to mesh objects with complex geometry by tetrahedra for high precision and mesh the surrounding space by square elements for simplicity and speed. In the discretization scheme of the DGTD method considered here, the electromagnetic field components are approximated by a high order nodal polynomial, using a centered approximation for the surface integrals. Time integration of the associated semi-discrete equations is achieved by a second or fourth order Leap-Frog scheme. After introducing the steps of the DGTD-PpQk method, I will expose the L2 stability analysis of this method (by establishing a sufficient CFL-like stability condition), and the theoritical convergence in h of the studied scheme, leading to a-priori error estimate. Afterward, I will present the numerical performances of the concerned method : a complete numerical study in 2D (for several test problems, on hybrid and non-conforming meshes, and for homogeneous or heterogeneous media), and the results of the 3D implementation, with more realistic simulations, for example the propagation in a heterogeneous human head model. I will conlude by showing the consistency between the mathematical and numerical results of this DGTD-PpQk method, and its contribution in terms of accuracy and CPU time.

I will finish this seminar by making the connection with the project I am working on, in postdoc at LMA (supported by Del Duca Foundation, French Academy of Sciences), within the Waves and Imaging team (supervised by Dimitri Komatitsch, Paul Cristini and Cédric Bellis). I work on a spectral elements method, for large-scale inversion and imaging using seismic/acoustic waves, and high-performance computing.